Mathematics · Grade 7

Active learning ideas

Density and Mass

Active learning works for density and mass because the concept demands direct experience with measurement and comparison. Students need to measure mass and volume themselves to see how the ratio defines density, not just the numbers alone. Concrete, hands-on activities make abstract formulas tangible and correct common misunderstandings about weight and buoyancy.

• Ontario Curriculum Expectations
• Ontario Curriculum: Mathematics Grade 7, Number B1.4: Read, represent, compare, and order rational numbers, including positive and negative fractions and decimal numbers, and explain their meaning in various contexts.
• Ontario Curriculum: Mathematics Grade 7, Number B1.6: Describe and represent the properties and relationships between the subsets of numbers, including whole numbers, integers, and rational numbers, using a variety of tools and strategies.
• Ontario Curriculum: Mathematics Grade 7, Number B1.2: Compare and order integers, decimal numbers, and fractions, including those with different denominators, in various contexts.

• 30–50 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Case Study Analysis
• 30 min · Pairs

Pairs: Density Calculation Lab

Partners select classroom objects, measure mass using a balance and volume by water displacement or ruler. They calculate density with the formula and record in a shared table. Discuss which objects might float based on results.

Explain the relationship between density, mass, and volume.

Facilitation Tip

In the Density Calculation Lab, circulate to ensure pairs measure volume accurately using water displacement, not just guessing by dimensions.

What to look for

Provide students with three objects (e.g., a small rock, a piece of wood, a metal bolt) and their masses. Have students measure the volume of each object using water displacement. Ask them to calculate the density of each object and record it on a worksheet.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Activity 02

• Case Study Analysis
• 45 min · Small Groups

Small Groups: Float or Sink Challenge

Groups predict if five objects will float or sink, then test in a water tub and measure densities to verify. Chart predictions versus outcomes and explain discrepancies using the density formula. Share findings with the class.

Predict whether an object will float or sink based on its density.

Facilitation Tip

For the Float or Sink Challenge, listen as groups explain their predictions before testing, guiding them to connect shape and air pockets to density.

What to look for

On an exit ticket, ask students to write the formula for density. Then, present a scenario: 'An object has a mass of 50g and a volume of 25cm³. Will it float or sink in water? Explain your reasoning.'

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Activity 03

• Case Study Analysis
• 35 min · Whole Class

Whole Class: Density Rainbow Column

Prepare layers of liquids with different densities like oil, water, syrup. Class adds objects to observe positions and calculates average densities. Discuss how this models ocean layers or fuel tanks.

Analyze how density is used in various scientific and engineering applications.

Facilitation Tip

During the Density Rainbow Column activity, ask students to predict where each liquid will settle before pouring to encourage proportional reasoning.

What to look for

Pose the question: 'Imagine you have two balls of the exact same size, one filled with feathers and one filled with sand. Which ball is denser and why? How does this relate to the mass and volume of each ball?' Facilitate a class discussion to solidify understanding.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Activity 04

• Case Study Analysis
• 50 min · Individual

Individual: Engineering Design Brief

Students design a floating raft from recyclables, calculate its density, and test load capacity. Adjust design based on trials and document mass, volume, density changes.

Explain the relationship between density, mass, and volume.

What to look for

Provide students with three objects (e.g., a small rock, a piece of wood, a metal bolt) and their masses. Have students measure the volume of each object using water displacement. Ask them to calculate the density of each object and record it on a worksheet.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

A few notes on teaching this unit

Teaching density works best when you start with objects students can hold and compare, moving from concrete to abstract. Avoid teaching the formula in isolation; instead, use it as a tool to explain observations. Research shows that students grasp density more deeply when they measure and calculate it themselves, rather than just being told the formula.

Successful learning looks like students confidently using the density formula, rearranging it to solve for missing values, and explaining why objects float or sink based on calculated densities. They should connect their calculations to real-world examples and communicate their reasoning clearly in discussions and written responses.

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Watch Out for These Misconceptions

• During the Density Calculation Lab, watch for students who assume density is the same as mass or weight.

  Have students compare two objects of similar mass but different volumes, such as a small metal bolt and a larger wooden block. Ask them to calculate each density and observe that the larger object can have a lower density despite its mass, using the formula as evidence.

• During the Float or Sink Challenge, watch for students who believe objects float if they are lighter than water regardless of volume.

  Provide objects of the same mass but different shapes, such as a solid ball of clay and a clay boat. Ask students to predict and then test which sinks and which floats, guiding them to see how volume and shape affect average density and buoyancy.

• During the Engineering Design Brief activity, watch for students who assume all metals sink because they are heavy.

  Have students build simple hollow models using aluminum foil or thin plastic. Ask them to calculate the average density of their model and test if it floats, showing how volume from air pockets lowers overall density.

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Methods used in this brief

• Case Study Analysis